Modeling Chilean Mathematics Teachers’ Instructional Beliefs on Problem Solving Practices

  • Farzaneh Saadati
  • Gamal Cerda
  • Valentina Giaconi
  • Cristian Reyes
  • Patricio Felmer


This study was designed to examine predictors of instructional beliefs related to problem solving that influence mathematics in-service teachers’ practices in the Chilean context. A total of 713 in-service mathematics teachers from various elementary schools participated in the survey study during 2015 and 2016. Results showed that teachers’ traditional beliefs are directly associated with their teacher-centered practices, while there was an indirect relation among reformed beliefs and student-centered practices through teachers’ self-efficacy beliefs and their beliefs about the value of problem solving. This association among beliefs and practices suggests that educators and policy makers should be aware of, when designing a teacher professional development, the need to emphasize other variables such as teachers’ self-efficacy and value of the task.


Classroom practices Instructional beliefs Mathematics problem solving Self-efficacy Structural equation modeling Value of problem solving 



The authors are thankful to the ARPA team—mentors, teachers, and researchers, specially Dr Lisa Darragh—for their support and interest in this work.

Funding Information

Funding from FONDEF ID14I20338 and PIA-CONICYT Basal Funds for Centers of Excellence Project FB0003 is gratefully acknowledged. VG thanks the CONICYT-PCHA/Doctorado Nacional/2013 21130684. FS is also grateful to the support of CONICYT/Fondecyt Postdoctoral Project 3170673.


  1. Ávalos, B., & De Los Rios, D. (2013). Reform environment and teacher identity in Chile. In D. B. Napier & S. Majhanovich (Eds.), Education, dominance and identity (pp. 153–175). Rotterdam: Sense.CrossRefGoogle Scholar
  2. Ávalos, B., & Matus, C. (2010). La formación inicial docente en Chile desde una óptica internacional. Informe nacional del Estudio Internacional IEA TEDS-M [Initial training in Chile from an international perspective. National Report of International Study of IEA TEDS-M]. Santiago: Ministerio de Educación.Google Scholar
  3. Ávalos, B., & Valenzuela, J. P. (2016). Education for all and attrition/retention of new teachers: A trajectory study in Chile. International Journal of Educational Development, 49, 279–290.CrossRefGoogle Scholar
  4. Ayarza, R. O., Soto, D. S., & Crocci, H. S. (2007). Renovación de la enseñanza del álgebra elemental: Un aporte desde la didáctica [Renewing the teaching of elementary algebra: A contribution of didactics]. Estudios Pedagógicos (Valdivia), 33(2), 81–100.Google Scholar
  5. Bandalos, D. L. (2002). The effects of item parceling on goodness-of-fit and parameter estimate bias in structural equation modeling. Structural Equation Modeling, 9(1), 78–102.CrossRefGoogle Scholar
  6. Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W H. Freeman.Google Scholar
  7. Bellei, C., & Morawietz, L. (2016). Strong content, weak tools twenty-first-century competencies in the Chilean educational reform. In F. M. Reimers & C. Chung (Eds.), Teaching and learning for the twenty-first century: Educational goals, policies, and curricula from six nations (pp. 93–125). Cambridge: Harvard Education Press.Google Scholar
  8. Bellei, C., & Vanni, X. (2015). Chile: The evolution of educational policy, 1980–2014. In S. Shwartzman (Ed.), Education in South America: Education around the world (pp. 179–200). London: Bloomsbury.Google Scholar
  9. Bent, G. J., Bakx, A., & Den Brok, P. (2017). Primary education teachers’ self-efficacy beliefs for teaching geography lessons. International Research in Geographical and Environmental Education, 26(2), 150–165.CrossRefGoogle Scholar
  10. Blömeke, S., & Kaiser, G. (2014). Theoretical framework, study design and main results of TEDS-M. In S. Blömeke, F. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 19–48). Dordrecht, The Netherlands: Springer.Google Scholar
  11. Bong, M. (2001). Role of self-efficacy and task-value in predicting college students’ course performance and future enrollment intentions. Contemporary Educational Psychology, 26(4), 553–570.CrossRefGoogle Scholar
  12. Burkhardt, H. (2006). Modelling in mathematics classrooms: Reflections on past developments and the future. ZDM, 38(2), 178–195.CrossRefGoogle Scholar
  13. Byrne, B. (2010). Structural equation modeling using AMOS: Basic concepts, applications, and programming (2nd ed.). New York: Taylor and Francis Group.Google Scholar
  14. Cárcamo, R. A., & Castro, P. J. (2015). Concepciones sobre el Aprendizaje de Estudiantes de Pedagogía de la Universidad de Magallanes y Docentes en Ejercicio en la Educación Básica de la ciudad de Punta Arenas, Chile [Conceptions about learning among pre-service students in University of Magallanes and in-service elementary teachers in Punta Arenas, Chile]. Formación Universitaria, 8(5), 13–24.CrossRefGoogle Scholar
  15. Carrillo, J. (1998). Exploring relationships between teachers’ conceptions and problem solving modes in mathematics. In E. Pehkonen & G. Törner (Eds.), The state of art in mathematics-related beliefs research. Helsinki, Finland: University of Helsinki.Google Scholar
  16. Chen, I. (2009). Behaviorism and developments in instructional design and technology. In P. Rogers, G. Berg, J. Boettcher, C. Howard, L. Justice, & K. Shenck (Eds.), Encyclopedia of distance learning (pp. 153–173). Hershey: Idea Group Incorporated.CrossRefGoogle Scholar
  17. Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18(8), 947–967.CrossRefGoogle Scholar
  18. Contreras, S. A. (2009). Creencias curriculares y creencias de actuación curricular de los profesores de ciencias chilenos [Chilean sciences teachers’ beliefs about curriculum and its performance]. Revista Electrónica de Enseñanza de las Ciencias, 8(2), 505–526.Google Scholar
  19. Cooney, T. J. (1994). Research and teacher education: In search of common ground. Journal for Research in Mathematics Education, 25(6), 608–636.CrossRefGoogle Scholar
  20. Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), Handbook of competence and motivation (pp. 105–121). New York: Guilford Press.Google Scholar
  21. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J., & Midgley, C. (1983). Expectancies, values and academic behaviors. In J. T. Spence (Ed.), Achievement and achievement motives (pp. 75–146). San Francisco: Freeman.Google Scholar
  22. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132. Scholar
  23. Eccles, J. S., Wigfield, A., & Schiefele, U. (1998). Motivation to succeed. In W. Damon & N. Eisenberg (Eds.), Handbook of child psychology: Social, emotional, and personality development (vol. 3, 5th ed., pp. 1017–1095). Hoboken: Wiley.Google Scholar
  24. Evers, W. J., Brouwers, A., & Tomic, W. (2002). Burnout and self-efficacy: A study on teachers’ beliefs when implementing an innovative educational system in the Netherlands. British Journal of Educational Psychology, 72(2), 227–243.CrossRefGoogle Scholar
  25. Farmer, J. A., Buckmaster, A., & LeGrand, B. (1992). Cognitive apprenticeship: Implications for continuing professional education. New Directions for Adult and Continuing Education, 1992(55), 41–49.CrossRefGoogle Scholar
  26. Feather, N. T. (1992). Values, valences, expectations, and actions. Journal of Social Issues, 48(2), 109–124.CrossRefGoogle Scholar
  27. Felbrich, A., Kaiser, G., & Schmotz, C. (2014). The cultural dimension of beliefs: An investigation of future primary teachers’ epistemological beliefs concerning the nature of mathematics in 15 countries. In S. Blömeke, F. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 209–230). Dordrecht: Springer.CrossRefGoogle Scholar
  28. Felmer, P., Lewin, R., Martínez, S., Reyes, C., Varas, L., Chandía, E., . . . Ortíz, A. (2014). Primary mathematics standards for pre-service teachers in Chile: A resource book for teachers and educators (Series on Mathematics Education, Vol. 9). Hackensack: World Scientific Printers.Google Scholar
  29. Felmer, P., & Perdomo-Díaz, J. (2016). Novice Chilean secondary mathematics teachers as problem solvers. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds), Posing and solving mathematical problems (pp. 287–308). Cham: Springer International Publishing.Google Scholar
  30. Flake, J. K., Barron, K. E., Hulleman, C., McCoach, B. D., & Welsh, M. E. (2015). Measuring cost: The forgotten component of expectancy-value theory. Contemporary Educational Psychology, 41, 232–244.CrossRefGoogle Scholar
  31. Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50.CrossRefGoogle Scholar
  32. Grootenboer, P., & Marshman, M. (2016). The affective domain, mathematics, and mathematics education. In P. Grootenboer & M. Marshman (Eds.), Mathematics, affect and learning (pp. 13–33). Singapore: Springer.CrossRefGoogle Scholar
  33. Guskey, T. R. (2002). Professional development and teacher change. Teachers and Teaching, 8(3), 381–391.CrossRefGoogle Scholar
  34. Handal, B. (2003). Teachers’ mathematical beliefs: A review. The Mathematics Educator, 13(2), 47–57.Google Scholar
  35. Hooper, D., Coughlan, J., & Mullen, M. (2008). Structural equation modelling: Guidelines for determining model fit. Electronic Journal of Business Research Methods, 6(1), 53–60.Google Scholar
  36. Jonassen, D. H. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45(1), 65–94.CrossRefGoogle Scholar
  37. Kang, M., & Byun, H. P. (2001). A conceptual framework for a web-based knowledge construction support system. Educational Technology, 41(4), 48–53.Google Scholar
  38. Keys, C. W., & Bryan, L. A. (2001). Co-constructing inquiry-based science with teachers: Essential research for lasting reform. Journal of Research in Science Teaching, 38(6), 631–645.CrossRefGoogle Scholar
  39. Kline, R. B. (2010). Principles and practice of structural equation modeling (3rd ed.). New York: Guilford Press.Google Scholar
  40. Leroy, N., Bressoux, P., Sarrazin, P., & Trouilloud, D. (2007). Impact of teachers’ implicit theories and perceived pressures on the establishment of an autonomy supportive climate. European Journal of Psychology of Education, 22(4), 529–545.CrossRefGoogle Scholar
  41. Ministry of Education Republic of Chile. (2012). Bases Curriculares Matemática; Ficha Bases Curriculares 2012. Santiago, Chile: Ministerio de Educación. Retrieved from
  42. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Retrieved from
  43. Organisation for Economic Co-operation and Developmen. (2012). Development co-operation report 2012. Paris, France: OECD Publishing.
  44. Peters, E. E. (2010). Shifting to a student-centered science classroom: An exploration of teacher and student changes in perceptions and practices. Journal of Science Teacher Education, 21(3), 329–349.CrossRefGoogle Scholar
  45. Polya, G. (1945). How to solve it (2nd ed., 1957). Princeton: Princeton University Press.Google Scholar
  46. Polya, G. (Ed.). (1981). Mathematical discovery: On understanding, learning, and teaching problem solving (Combined ed.). New York: Wiley.Google Scholar
  47. Powell-Moman, A. D., & Brown-Schild, V. B. (2011). The influence of a two-year professional development institute on teacher self-efficacy and use of inquiry-based instruction. Science Educator, 20(2), 47–53.Google Scholar
  48. Prawat, R. S. (1992). Teachers’ beliefs about teaching and learning: A constructivist perspective. American Journal of Education, 100(3), 354–395.CrossRefGoogle Scholar
  49. Preiss, D., Larraín, A., & Valenzuela, S. (2011). Discurso y pensamiento en el aula matemática Chilena [Discourse and thought in Chilean math classroom]. Psykhe, 20(2), 131–146.CrossRefGoogle Scholar
  50. Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550–576.CrossRefGoogle Scholar
  51. Ruffinelli, A. (2016). Ley de desarrollo profesional docente en Chile: de la precarización sistemática a los logros, avances y desafíos pendientes para la profesionalización [Law on teacher professional development: From systematic precariousness to the achievements, the advances, and the remaining challenges for professionalization]. Estudios Pedagógicos, 42(4), 261–279.CrossRefGoogle Scholar
  52. Sass, D. A., & Smith, P. L. (2006). The effects of parceling unidimensional scales on structural parameter estimates in structural equation modeling. Structural Equation Modeling, 13(4), 566–586.CrossRefGoogle Scholar
  53. Schiefele, U., & Schaffner, E. (2015). Teacher interests, mastery goals, and self-efficacy as predictors of instructional practices and student motivation. Contemporary Educational Psychology, 42, 159–171.CrossRefGoogle Scholar
  54. Schmeisser, C., Krauss, S., Bruckmaier, G., Ufer, S., & Blum, W. (2013). Transmissive and constructivist beliefs of in-service mathematics teachers and of beginning university students. In Y. Li & J. N. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics (pp. 51–67). Rotterdam: Sense.Google Scholar
  55. Schoenfeld, A. H. (1999). Models of the teaching process. The Journal of Mathematical Behavior, 18(3), 243–261.CrossRefGoogle Scholar
  56. Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226.CrossRefGoogle Scholar
  57. Swan, M. (2006). Designing and using research instruments to describe the beliefs and practices of mathematics teachers. Research in Education, 75(1), 58–70.CrossRefGoogle Scholar
  58. Tang, S. J., & Hsieh, F. J. (2014). The cultural notion of teacher education: Future lower secondary teachers’ beliefs on the nature of mathematics, the learning of mathematics and mathematics achievement. In S. Blömeke, F. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 231–253). Dordrecht: Springer.Google Scholar
  59. Tatto, M. T., Rodríguez, M., Ingvarson, L., Rowley, G., Maeda, Y., & Byun, S. Y. (2013). Development of the TEDS-M survey questionnaires. In M. T. Tatto (Ed.), Technical report of The Teacher Education and Development Study in Mathematics (TEDS-M) policy, practice, and readiness to teach primary and secondary mathematics in 17 countries (pp. 47–70). Amsterdam: International Association for the Evaluation of Educational Achievement (IEA).Google Scholar
  60. Thompson, A. G. (1985). Teachers’ conceptions of mathematics and the teaching of problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 281–294). Hillsdale: Erlbaum.Google Scholar
  61. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.Google Scholar
  62. Törner, G., Schoenfeld, A. H., & Reiss, K. M. (2007). Problem solving around the world: Summing up the state of the art. ZDM, 39(5–6), 353–353.CrossRefGoogle Scholar
  63. Tschannen-Moran, M., & Hoy, A. W. (2001). Teacher efficacy: Capturing an elusive construct. Teaching and Teacher Education, 17(7), 783–805.CrossRefGoogle Scholar
  64. Wigfield, A., Tonks, S., & Klauda, S. L. (2009). Expectancy-value theory. In K. R. Wentzel & A. Wigfield (Eds.), Handbook of motivation at school (pp. 55–75). New York: Routledge Taylor & Francis Group.Google Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2018

Authors and Affiliations

  1. 1.Centro de Investigación Avanzada en Educación (CIAE)Universidad de ChileSantiagoChile
  2. 2.Departamento es de Metodología de la Investigación e Informática Educativa, Facultad de EducaciónUniversidad de ConcepciónConcepciónChile
  3. 3.Instituto de Ciencias de la EducaciónUniversidad de O’HigginsRancaguaChile
  4. 4.Center for Mathematical Modeling (CMM)Universidad de ChileSantiagoChile

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